B M Sharma Solutions for Chapter: Fluid Mechanics, Exercise 1: CONCEPT APPLICATION EXERCISE

Three containers filled to the same height with the fluid of same density as shown in figure. In which container, if any, is the pressure at the bottom greatest?

In a U-tube which is open at both ends, two liquids, $1$ and $2,$ are in equilibrium, as shown in the figure. If the liquids do not mix and liquid $1$ rests on top of liquid $2,$ then how is the density ${\rho }_1$ of liquid $1$ related to the density ${\rho }_2$ of liquid $2?$

A hole of area $5{ \mathrm{cm}}^2$ is formed in the side of a ship $3 \mathrm{m}$ below the water level. What minimum force is required to hold on a patch covering the hole from the inside of the ship?

What will be the length of mercury column in a barometer tube, when the atmospheric pressure is $75 \mathrm{cm}$ of mercury and the tube is inclined at an angle of $60°$ to the vertical?

How high would water rise in the pipes of a building, if the water pressure gauge shows the pressure at the ground floor to be $270 \mathrm{kPa}?$

Torricelli's barometer used mercury. Pascal duplicated it using alcohol of density $984 \mathrm{kg}{ \mathrm{m}}^{-3}.$ Determine the height of the alcohol column for normal atmospheric pressure. (Given normal atmospheric pressure, $P_{\mathrm{atm} }=1.013\times {10}^5$ ${\mathrm{Nm}}^{-2}$)

The gauge pressure in both the tyres of a bicycle $6.0\times {10}^5 \mathrm{Pa}.$ If the bicycle and the person riding it have a combined mass of $90 \mathrm{kg},$ what is the area of contact of each tyre with the ground?

A hydraulic automobile lift has input and output pistons with diameters of $10 \mathrm{cm}$ and $30 \mathrm{cm}.$ The lift is used to hold up a car with a weight of $144\times {10}^4 \mathrm{N}.$
(a) What is the force on the input piston?
(b) What pressure is applied on the input piston?